where \(\, L(f,s)= \sum _{ \mathfrak {D}^{-1}/ U^+ \ni \nu \succ 0 }\frac{a_f(\nu )}{\mathcal {N}(\nu )^s} \, \, \, ( Re (s) \gg 0 ).\)   
It is well-known that \(\Lambda (f, s)\)  has an analytic continuation and functional equation [1]}, [2]}
\(\Lambda (f, s)= (-1)^{\frac{tk}{2}} \Lambda (f, k-s).\) 
